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Big Ideas Math: Modeling Real Life - Kindergarten

Big Ideas Learning, LLC | Kindergarten

Alignment: Overall Summary

The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten partially meet the expectations for alignment. The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials partially meet the expectations for Gateway 2, rigor and practice-content connections. The materials meet the expectations for rigor by reflecting the balances in the Standards and giving appropriate attention to conceptual understanding and procedural skill and fluency. The materials partially meet expectations for practice-content connections. The materials identify the \practices and attend to the specialized language of mathematics, however, they do not attend to the full intent of the practice standards.

The Report

Gateway One

Focus & Coherence

Meets Expectations

The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet the expectations for Gateway 1, focus and coherence. Assessments represent grade-level work, and items that are above grade level can be modified or omitted. Students and teachers using the materials as designed would devote a majority of time to the major work of the grade. The materials are coherent and consistent with the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet the expectations that the materials do not assess topics from future grade levels. The instructional materials do contain assessment items that assess above grade-level content, but these can be modified or omitted.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten meet the expectations for assessing grade-level content. Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

Chapter 8, Test A and Test B, Question 6, students write an "addition sentence" to match a given word problem. The matching addition sentences are 10 + 3 = 13 and 10 + 5 = 15 respectively. This is beyond the standard K.OA.2, solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Chapter 10, Test A and Test B, Question 6, students circle the number that represents the amount of bouncy balls using groups of 10s and 1s with solutions of 46 and 53 respectively. This aligns to 1.NBT.2.

Chapter 10, Test A and Test B, Questions 1-4, students fill in the missing numbers on a 100s chart by circling the missing numbers. (K.CC.1)

Chapter 10, Test A and Test B, Question 5, students fill in the missing numbers on a 100s chart when counting by ten from a given number. (K.CC.A)

Chapter 11, Test A and Test B, Question 6, “Use squares and rectangles to draw 5 windows and 1 door on the castle. Color the castle. Then write an 'addition sentence' to tell how many squares and rectangles you drew in all.” Test B states, “Use squares and rectangles to draw 6 windows and 1 door on the castle.” (K.OA.1)

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.

The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet the expectations for spending a majority of class time on major work of the grade when using the materials as designed. Time spent on the major work was figured using chapters, lessons, and days. Approximately 71% of the time is spent on the major work of the grade.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten meet expectations for spending a majority of instructional time on major work of the grade. For Kindergarten, this includes all clusters within K.OA, K.NBT, and K.CC.

To determine the focus on major work, three perspectives were evaluated: the number of chapters devoted to major work, the number of lessons devoted to major work, and the number of weeks devoted to major work.

The approximate number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 9 out of 13, which is approximately 69% of the instructional time.

The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 68 out of 96, which is approximately 71% of the instructional time.

The number of days devoted to major work (including assessments and supporting work connected to the major work) is 105 out of 148 days, which is approximately 71% of the instructional time.

A day-level analysis is most representative of the instructional materials because the number of days is not consistent within chapters and lessons. As a result, approximately 71% of the instructional materials focus on the major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten meet the expectations that the materials are coherent and consistent with the standards. The materials represent a year of viable content. Teachers using the materials would give their students extensive work in grade-level problems, and the materials describe how the lessons connect with the grade-level standards. However, above grade-level content is present and not identified.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of the connections between supporting work and major work include the following:

Chapter 4, Lesson 5, Think and Grow, connects K.MD.3 to major work K.CC.6 when students show a number of vehicles IN the water and number OUT of the water in the picture, then circle the category with the greater number of vehicles. Students connect to major work by writing a total number in each category (K.CC.3) before circling which number is greater (K.CC.7).

Chapter 11, Lesson 1, Think and Grow, connects supporting standard K.G.4 to major work K.CC.5 and K.CC.3 when students count shapes to answer questions such as, “How many stickers in the picture have more than 4 vertices?”

Chapter 11, Lesson 2, Think and Grow, connects supporting standard K.G.5 to major work K.CC.5 when students draw and color 10 triangle-shaped flags. This problem is also connected to major work K.OA.1 when students write an equation to match the picture.

Chapter 11, Lesson 6, Think and Grow, connects supporting standard K.G.6 to major work K.CC.5 when students use pattern blocks to trace and create a new shape, then count and write how many pattern blocks they used.

Chapter 12, Lesson 4, Think and Grow, students connect supporting standard K.G.5 to major work K.CC.5 when students draw the shape of the flat surfaces of a cylinder, then count and write the number of flat surfaces.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

Instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet expectations that the amount of content designated for one grade-level is viable for one year.

As designed, the instructional materials can be completed in 148 days with each lesson counting as one day. The minimum time per class period is 45 minutes, with the recommended time of 60-70 minutes. A pacing guide can be found in the Teachers Guide. Kindergarten is divided into 13 Chapters. The 148 days include the following:

96 days of Lessons.

13 days of Lesson Opener Activities - Each Chapter begins with a chapter opener.

26 days for “Connect and Grow” Activities - Two days per chapter are dedicated to these activities which include a performance task and chapter practice on one day and centers on the other day.

13 days for Chapter Assessments - Each chapter has a final chapter assessment.

Indicator 1e

Materials are consistent with the progressions in the Standards
i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work
ii. Materials give all students extensive work with grade-level problems
iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten partially meet expectations for being consistent with the progressions in the Standards. The presence of above grade-level content distracts from all students engaging with extensive work of the grade.

The Teacher Edition includes a “Progression Through the Grades” chart which outlines each domain and its accompanying clusters, and which chapters address each cluster. Additionally, tables are provided to identify which lessons address specific standards. The beginning of each chapter includes an overview table “Progressions Through the Grades” that shows the content from the previous and future grade levels, and “Laurie’s Overview” where the math in the chapter is explained and connected to prior and future work of the grade. For example:

The "Progression Through the Grades" chart states: Kindergarten “Name, count, and write numbers within 5. Pair each number name with an object. Determine that the last number stated names the total. Count objects in different arrangements. Order numbers within 5 both forward and backward. Understand that the next number stated is one number greater. “ Grade 1 “Represent, write, and solve ‘Add To’ and ‘Put Together’ problems with unknowns. Write and solve addition number sentences. Solve addition word problems. Represent, write, and solve ‘Take From’ and ‘Take Apart’ problems with unknowns. Write and solve subtraction number sentences. Solve subtraction word problems. Solve addition and subtraction comparison problems.”

The instructional materials develop according to the grade-by-grade progressions. For example, in the Teacher Edition, Chapter 6, Lesson 3, addresses Standard K.CC.5:

Explore and Grow: “Directions: Use counters to act out the story. There are 4 pencils in the case. Write the number. There are 3 crayons in the case. Write the number. Tell how many objects are in the case now.”

Think and Grow: “Directions: Circle the groups to put them together. Then write an addition sentence to tell how many objects there are in all.”

Apply and Grow Practice: “Directions: Circle the groups to put them together. Then write an addition sentence to tell how many objects there are in all.”

Think and Grow: Modeling Real Life: “Directions: You have 5 balls of red clay and 1 ball of blue clay. Draw and color the balls of clay. Then write an addition sentence to tell how many balls of clay you have in all.”

Practice: additional practice problems are included.

Throughout the instructional materials, above grade-level content is present. This content is not identified as above grade-level, and distracts students from engaging with extensive work with grade-level mathematics to meet the full intent of grade-level standards. For example:

Chapter 9, Lesson 6, Think and Grow, “Compare the numbers of red dots and blue dots. Circle the number that is greater than the other number.” Followed by, “Compare the numbers of yellow dots and red dots. Draw a line through the number that is less than the other number.” The numbers used are “20 and 17” and “14, 18, and 11.” (1.NBT.3)

Lesson 5, Explore and Grow, students “circle the number that shows how many”, but the picture has groups of tens and ones. (1.NBT.2)

Lessons 6, Explore and Grow, students count by tens “off the decade” (1.NBT.1). In the Think and Grow, students start counting from a number other than 10. Students “count the milk cartons. Circle the number that tells how many. (25)" This is presented in two groups of 10 and 5 ones.

Each Unit contains an “About the Math” section that connects the math to prior knowledge. Laurie’s Notes: Preparing to Teach connects prior knowledge to the content of the lesson. For example:

Teacher Edition, Chapter 1, Lesson 1, Laurie’s Notes, Preparing to Teach, “Many students are able to orally count numbers, meaning they can recite the sequence one, two, three, and so on. A second and different skill is connecting the sequence of the words one, two, three and so on in a one-to-one correspondence with objects being counted. In this first lesson, students use one-to-one correspondence to count one or two objects and tell how many objects are in a group. They should understand that the last number they count is the total number of objects.”

Teacher Edition, Chapter 2, Lesson 2, Laurie’s Notes, Preparing to Teach, “Give two students unequal amounts of snacks and they will know it! They can usually tell when the quantities are the same as, or equal. Students compare groups of objects by matching each object from one group to an object from another group. When matching, students can see if each object has a 'partner'. The term 'partner' helps students recognize when two groups of quantities are the same. This also prepares students to recognize quantities that are odd or even.”

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards
i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings.
ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, and they provide problems and activities that connect two or more clusters in a domain or two or more domains when the connections are natural and important.

Chapter 2, Lesson 3, Apply and Grow, “Show and tell whether one group has a lesser number of objects than another group.” Students use counters to show the number of rabbits and to show the number of rabbit holes. Students are then asked are there fewer rabbits or fewer holes. This is shaped by the cluster heading K.CC.C.

Chapter 8, Lesson 11, Apply and Grow, “Understand the numbers 18 and 19.” Students circle 10 objects, then draw dots in a 10-frame to show how many objects are circled. Then students draw dots in the bottom ten frame to show how many more objects there are. They complete a number sentence to match the drawing (example: 19=10+9). This is framed by the cluster heading K.NBT.A.

Chapter 8, Lesson 3, Apply and Grow, the learning objective is visibly shaped by the cluster heading K.NBT.A. For example, “Directions: Circle 10 objects. Draw dots in the ten frame to show how many more objects are circled. Draw dots in the five frame to show how many more objects that are. Use the frames to write an addition sentence.”

Examples of problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, include:

Chapter 3, Lesson 2, Think and Grow, connects knowing number names and the count sequence (K.CC.A) and count to tell the number of objects (K.CC.B). For example, “Directions: Count the objects. Say the number. Trace and write the number. Count the instruments. Say the number. Write the number.”

Chapter 4, Lesson 2, Think and Grow, connects count to tell the number of objects (K.CC.B) with compare numbers (K.CC.C). For example in Question 2, students “count the number of objects in each group. Write the number. Circle the number that is greater than the other number.”

Chapter 4, Lesson 5, Think and Grow, students “Show the number of vehicles in the water and the number of vehicles NOT in the water. Circle the category with the greater number of vehicles.” This connects comparing numbers (K.CC.C) to classifying objects and counting the number of objects in each category (K.MD.B).

Chapter 5, Lesson 1, Think and Grow, connects major cluster headings understand addition as putting together and adding to, and understand subtraction as taking apart and taking from (K.OA.A) and count to tell the number of objects (K.CC.B). For example, “Directions: 3 and 4 Count each type of dog. Write each number. Count all of the dogs. Write the number for the whole.”

Chapter 8, Lesson 7, Think and Grow, connects working with numbers 11-19 to gain foundations for place value (K.NBT.A) with counting to tell the number of objects (K.CC.B) and knowing number names and the count sequence (K.CC.A) by having the students “Circle ten flowers. Draw dots in the top ten frame to show how many flowers are circled. Draw dots in the bottom ten frame to show how many more flowers there are. Use the ten frames to write an addition sentence.”

Chapter 12, Lesson 5, Think and Grow, students “Use your materials to build one of the three-dimensional shapes shown. Circle the three-dimensional shape that you build.” This connects the clusters identify and describe shapes (K.G.A) and analyze, create, compare, and compose shapes (K.G.B).

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten partially meet the expectations for rigor and mathematical practices. The materials partially meet the expectations for rigor by reflecting the balances in the Standards and giving appropriate attention to procedural skill and fluency. The materials partially meet the expectations for practice-content connections, they identify the Standards for Mathematical Practices, and attend to the specialized language of mathematics, but do not attend to the full intent of each practice standard.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten meet the expectations for rigor and balance. The instructional materials give appropriate attention to conceptual understanding and procedural skill and fluency, and the materials address these three aspects with balance, not always treating them separately and not always together.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

At the beginning of each chapter, Laurie’s Notes identify a whole group lesson with a manipulative or specific strategy to develop conceptual understanding. The Explore and Grow “give students a hands-on approach to develop conceptual understanding.”

Cluster K.CC addresses representing addition and subtraction with objects, fingers, mental images, etc. Many lessons in Chapters 1-7 explore ways to develop and independently demonstrate conceptual understanding of adding and subtracting using different representations. Examples from these chapters include:

Chapter 1, Lesson 6, Explore and Grow, the teacher reads the book “At The Pond.” After reading, students look at the page in their math book with a log and a pond. Students use counters to show how many turtles are in the story, then write the number of how many turtles are in the story (5). This develops understanding the relationship between numbers and quantities; connect counting to cardinality (K.CC.4) and writing numbers from 0 to 20 (K.CC.3).

Chapter 2, Lesson 1, Think and Grow, students “Draw paint spots so that the numbers of paint tubes and paint spots are not equal. Draw lines between the objects in each group to show that you are correct.” This develops understanding of identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (K.CC.6).

Chapter 3, Lesson 11, Apply and Grow, students “Place counters in the ten frame as you count forward to 10. Trace and write the missing numbers.” This develops the understanding when counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object (K.CC.4a).

Chapter 4, Lesson 3, Think and Grow, students “Compare the numbers. Draw a line through the number that is less than the other number. Draw to show how you know.” For example, students compare 8 and 4 by drawing circles to represent each number, and draw lines to match them together to see which has more. This develops understanding of identifying whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (K.CC.6).

Chapters 5, 6, and 7 address K.OA.A, understand addition and subtraction as putting together and adding to, and understand subtraction as taking apart and taking from. The materials provide opportunities for students to develop conceptual understanding and independently demonstrate their understanding. For example:

Chapter 5, Lesson 3, Think and Grow, students solve, “There are 6 tomatoes at a farm stand. Newton and Descartes buy all of them. Newton buys fewer tomatoes than Descartes.” Students have the opportunity to show a variety of answers such as “5 + 1 = 6; 2 + 4 = 6”, etc. K.OA.3. (Decompose numbers less than or equal to 10 into pairs in more than one way.)

Chapter 5, Lesson 5, Think and Grow, students solve, “Put the marbles into 2 groups. Circle the groups. Then complete the number bond to match your picture.” Students circle “4 + 4 = 8” or “5 + 3 = 8”, etc. K.OA.3. (Decompose numbers less than or equal to 10 into pairs in more than one way.)

Chapter 6, Lesson 1, Explore and Grow, directions, “Use counters to act out the story. There are 3 students on the bus. Write the number. 2 more students get on the bus. Write the number. Tell how many students are on the bus now.” This supports conceptual understanding as it aligns with K.OA.1, as students show the mathematics using counters.

Chapter 6, Laurie’s Notes (2nd bullet under Additional Support), “Ask students to use their fingers on both hands to represent the whole. The fingers on each hand are the partner numbers for the whole.” This supports conceptual understanding of K.OA.1, because students represent addition with fingers.

Chapter 7, Laurie’s Notes (Teaching Notes, Supporting Learners), “Each problem can be modeled using a five frame and counters, using fingers, or having students act it out.” This supports conceptual understanding of K.OA.1, because students subtract using objects, fingers, and acting out.

Chapter 7 Lesson 2, Think and Grow, students solve “Some bats in a cave fly away. Cross out the bats that fly away….” Students cross out 8 of 9 bats. This supports conceptual understanding of K.OA.1, because students subtract using objects.

Within the Apply and Grow and Homework and Practice sections, students have opportunities to independently demonstrate conceptual understanding. For example:

Chapter 6, Lesson 3, Apply and Grow, Practice, students “Circle the groups to put them together. Then write an addition sentence to tell how many objects there are in all.” Problem 2 shows 3 red balls and 5 yellow cubes.

Chapter 9, Lesson 6, Apply and Grow, Practice, students “Count the objects in each group. Write each number.” Problem 2, “Circle the number that is greater than the other number.” Students have a group of 12 yellow balls and 11 red balls.

Chapter 12, Lesson 2, Practice, Problem 1, students “Look at the solid shapes on the left that stack. Circle the other solid shapes that stack.” Students are given a cylinder, cube, and ball.

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet expectations that they attend to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency, especially where called for by the Standards, and present opportunities for students to independently demonstrate procedural skill and fluency.

In Explore and Grow, there is “teacher-guided instruction with opportunities for student involvement to ensure all levels of learners attain procedural fluency.” Apply and Grow Practice presents some opportunities for independent practice to allow students to further their procedural skills.

The instructional materials present opportunities for students to develop procedural skill and fluency, especially for K.OA.5 (Fluently add and subtract within 5). For example:

Chapter 6, Lesson 6, Apply and Grow, “Complete the addition sentence. Tell how you found your answer. Complete the addition sentences. Tell what you notice.” In Laurie’s Notes, Preparing to Teach, “This is the first section in Kindergarten where the focus is on fluency.”

Chapter 7, Lesson 5, Apply and Grow Practice, subtraction within 5. “Complete the subtraction sentence. Tell how you found your answer. Circle all of the subtraction problems that equal 3.”

Chapter 7, Lesson 6, Think and Grow, students write an addition or subtraction equation based on a picture. “Tell whether the pictures show addition or subtraction. Then write the addition or subtraction sentences to show the related facts.”

Chapter 7, Lesson 7, Explore and Grow, “You have 3 yellow linking cubes and 2 green linking cubes. How many linking cubes do you have in all? Write an addition sentence to match the picture. You have 5 linking cubes. You give your friend 2 linking cubes. How many linking cubes do you have left? Write a subtraction sentence to match the picture.”

Online Skills Trainer provided one section that addresses K.OA.5.

One Center game, “Numberland”, has addition and subtraction facts to 5 (K.OA.5).

Students independently demonstrate procedural skill and fluency in some lessons, while most online Center Games present opportunities for students to practice procedural skills and fluency. These include:

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten partially meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

The Think and Grow: Modeling Real Life section in each lesson “brings problem solving into the classroom.” Standard K.OA.2, Solve addition and subtraction word problems, and add and subtract within 10, is addressed in Chapters 6 and 7. Students engage with routine application problems, including add to/take from, as well as put together/take apart problems. The following are examples of materials engaging students in application of the K.OA.2:

Chapter 6, Lesson 1, Think and Grow, students add to with result unknown, “5 students are playing basketball. 5 more students join them. Draw the students who join them. Then complete the sentence to tell how many students are in the group to start, how many join them, and how many there are in all.”

Chapter 6, Lesson 3, Think and Grow, has two “put together with total unknown” problems. For example, “You have 5 balls of red clay and 1 ball of blue clay. Draw and color the balls of clay. Then write an addition sentence to tell how many balls of clay you have in all.”

Chapter 6, Lesson 8, Think and Grow, students solve addition problems with one addend unknown. “You need 10 tickets in all to win a prize. You win 1 ticket. Draw more tickets to make 10. Then write an addition sentence to match your picture.”

Chapter 6, Performance Task, students solve problems with both addends unknown. “You buy more red fish than blue fish at a pet store. Color to show the fish that you buy. Then write an addition sentence to match your picture.”

Chapter 7, Lesson 2, Think and Grow, students solve three “take from” subtraction problems by telling how many animals are left and writing the sentence to match.

Chapter 7, Lesson 6, Think and Grow, has a “take from with result unknown” problem. “You have 2 rolls to knock down 10 bowling pins. On your first roll, you knock down 5 pins. Cross out the pins you knock down. Then write a subtraction sentence to match your picture.”

There are some examples of non-routine problems found in Chapter Performance Tasks, for example:

Chapter 7, Performance Task, students solve three subtraction problems on a page related to a picture of bubbles. Each problem builds from the one before. Question 2, “Some of the bubbles pop. Cross out the bubbles that pop. Then write a subtraction sentence to tell how many bubbles are left.” Question 3, “All of the remaining bubbles pop. Write a subtraction sentence to tell how many bubbles are left now.”

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

The instructional materials present opportunities for students to engage in each aspect of rigor, as well as multiple aspects of rigor, in each lesson. For example:

Chapter 1, Lesson 7, students develop conceptual understanding of zero. They guess the numbers on dot card models displaying 1-5. After a few rounds, the 0 card is displayed. Students are asked, “What can we call it when we have nothing?” Students then discuss examples of the quantity zero developing their understanding of 0. During the Explore and Grow, students hear a “Story Time” about an empty box. In the Think and Grow, students compare real-world objects that consist of “two tree limbs”. One tree limb has one leaf, the other has zero leaves. Students practice writing 0. In Apply and Grow Practice, students count fireflies in a jar, then write the numeral next to the jar.

Chapter 9, Lesson 6, Think and Grow: Modeling Real Life, students solve routine application problems to find “who has more.” For example, “You have 14 balls, Your friend has a number of balls that is 1 more than 12. Draw the balls. Write the numbers. Circle the number that is greater than the other number.”

Students have opportunities to engage in multiple aspects of rigor. For example:

Chapter 4, Lesson 1, Think and Grow, “Is the number of toothbrushes equal to the number of toothpaste tubes? Circle the thumbs up or thumbs down.”

Chapter 6, Lesson 4, Practice, Problem 4, “There are 6 paint spots on a paint tray. Some are purple and some are green. Color the paint spots to show partner numbers that make 6. Then color the paint spots to show another way to make 6. Write the addition sentence to match your pictures.”

Chapter 9, Lesson 3, Think and Grow: Modeling Real Life, “You have 20 coins in your piggy bank. You drop and break your piggy bank. Did you find all your coins? Circle the thumbs up for yes or the thumbs down for no.”

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten partially meet the expectations for practice-content connections. The materials identify the practice standards and explicitly attend to the specialized language of mathematics. However, the materials do not attend to the full meaning of each practice standard and do not provide opportunities to engage students in analyzing the arguments of others.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade-level.

The Standards for Mathematical Practice (MP) are identified in the digital Teacher's Edition on page vi. The guidance for teachers includes the title of the MP, how each MP helps students, where in the materials the MP can be found, and how it correlated to the student materials using capitalized terms. For example, MP2 states, "Reason abstractly and quantitatively.

"Visual problem-solving models help students create a coherent representation of the problem.

Explore and Grows allow students to investigate concepts to understand the REASONING behind the rules.

Exercises encourage students to apply NUMBER SENSE and explain and justify their REASONING."

The MPs are explicitly identified in Laurie’s Notes in each lesson, and are connected to grade-level problems within the lesson. For example:

In Chapter 1, Lesson 8, Think and Grow: Modeling Real Life, Laurie’s Notes, identifies MP3, Construct Viable Arguments and Critique the Reasoning of Others. For example, “Encourage students to count and then check with partners to see whether they agree about the number of each color star. Students should feel comfortable talking with partners and then self-correcting when they recognize a mistake.”

In Chapter 4, Lesson 3, Think and Grow, Laurie’s Notes, identifies MP8, Look for and Express Regularity in Repeated Reasoning as students compare numbers by drawing counters and pairing them for each number. Guidance for the teacher states “How did you compare 10 and 7?’ I know 10 comes after 7, so 10 is greater. ‘How did you compare 1 and 6?’ I know 6 comes after 1, so 6 is greater. If 6 is greater, then 1 is less.”

Chapter 5, Lesson 1, Laurie’s Notes, students show different ways to make a number. “Is there more than one way to make the number 5? How do you know?” (MP7).

The MPs are identified in the digital Student Dashboard under Student Resources, Standards for Mathematical Practice. This link takes you to the same information found in the Teacher Edition.

There are some instances where the MPs are over or under-identified. For example:

MP2 is identified in most lessons.

MP5 is under-identified in the materials.

MP8 is under-identified as students begin to generalize addition and subtraction as ‘add to’ and ‘take from’.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten do not meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

The instructional materials do not present opportunities for students to engage in MP4: Model with mathematics; MP5: Use appropriate tools strategically; MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning.

The instructional materials present few opportunities for students to model with mathematics (MP4). Throughout the materials, models are provided for students.

Chapter 4, Lesson 2, Think and Grow, MP4, “Have students use counters to model the numbers 6 and 8 in the ten frames.”

While the Dynamic Student Edition includes tools for students, the instructional materials present few opportunities for students to choose their own tool, therefore, the full meaning of MP5 is not being attended to. MP5 is not found in Chapters 1, 3, 4, 5, 6, 8, and 9. The

Chapter 7, Lesson 6, Laurie's Notes, Apply and Grow, identifies MP5. “Cross out 5 counters to show how many to take away. Use the ten frame to complete the subtraction sentence.”

Chapter 6 Lesson 5, identifies MP5. Students model (using base ten blocks) 2 tens and 3 ones. In the Teacher Edition the directions for teachers state, “I don’t want to have to continue to build towers. We are going to use a new tool today called base ten blocks. Tens are put together for us.”

MP7 is often presented in the instructional material with guidance telling students how to look for structure, thus limiting their opportunities to identify and use structures.

Chapter 8, Lesson 7, Explore and Grow, MP7. “There are different partner numbers for 15. Today we are learning about a special pair 10 and 5. Separate and place the two pieces on the number bond for the parts.”

Chapter 8, Lesson 1, Laurie’s Notes, Dig In, “We want to introduce a quantity in the teens as being a group of ten ones and some more ones. Some students know the counting names and will want to continue counting, eleven, twelve, and so on. Acknowledge their counting and comment on having more than ten ones.”

MP8 is identified in Chapters 5, 6, and 7, however, the materials present few opportunities for students to engage in repeated reasoning. For example:

Chapter 5, Lesson 8, Think and Grow, identifies MP8. Students use a number bond with a missing part and a ten frame with the same part missing. “Draw dots in the ten frame to make the whole. Use the ten frame to complete the number bond.” In the Teacher’s Edition, teachers ask, “What’s the same about each number bond?” (one part is 5).

Chapter 5, Lesson 8, Teaching Notes, MP8 is identified as “Look for and express regularity in repeated reasoning.” The directions state, “Does the whole change if a cherry falls to the ground? Explain.”

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

In Kindergarten, students engage in MP3 when directions ask them to make comparisons, or tell why they make a decision. For example:

Chapter 7, Lesson 7, Apply and Grow Practice, Problems 2 and 3, students “Circle the addition and subtraction sentences that show related facts. Tell how you know.”

Chapter 9, Lesson 6, students compare the numbers 13 and 15. The directions state, “Place linking cubes on the ten frames to show the numbers. Which number is greater than the other number? Which number is less than the other number?”

Chapter 12, lesson 3, Think and Grow: Modeling Real Life, “You stack the 3 objects shown. Write 1 below the object you place at the bottom of the stack, write 2 below the object you stack next, and write 3 below the object you stack last. Tell why you chose this order.”

Chapter 13, Lesson 5, Think and Grow: Modeling Real Life, students are given pictures of objects to compare: a desk and a notebook; and a bus and a lunchbox. Directions: “Circle the object you can carry. Tell why you can carry the object. Circle the object you cannot carry. Tell why you cannot carry the object.”

The instructional materials do not present opportunities in Kindergarten for students to analyze the thinking of others.

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

Chapter 6, Lesson 4, Laurie’s Notes, Think and Grow, MP3 is identified and the materials state, “It is very possible that a student will produce the work shown. Some students will say this is wrong because the addition sentence should be 4 = 1 + 3. Others will say it doesn’t matter if you write 1 + 3 or 3 + 1. The point is not to introduce the Commutative Property, rather give students the opportunity to think about the relationship and critique the reasoning of others.”

Chapter 7, Lesson 5, Laurie’s Notes, Think and Grow, MP3 is identified and the materials state, “When students share their thinking with classmates, ask other students to comment on what they have heard. ‘Do you agree with how (name) explained using your fingers to take away a number? Did their thinking make sense? Why?’”

Chapter 11, Lesson 2, Laurie’s Notes ,Think and Grow, MP3 is identified and the materials state, “Look around the room. Are there examples of triangles on the wall, clothing, books, and so on? Have students point to the object and explain why it is a triangle. Be sure to ask other students if they agree with the explanation or not.”

There are occasions where the materials do not provide guidance for teachers to engage students in MP3. Not all explanations require students to construct an argument or analyze the arguments of others. For example:

Chapter 5, Lesson 8, Laurie’s Notes, Think and Grow, MP3 is identified and the materials state, “Point to the number path. Have students Turn and Talk about using a number path for finding the other partner number.” This prompt does not support teachers to guide a discussion where students need to construct an argument and/or critique the reasoning of others.

Chapter 9, Lesson 6, Laurie’s Notes, Think and Grow, “(name), what did you circle and why? Be sure the student explains how they knew their friend had 13 balls.” This does not support the teacher in helping students critique the reasoning of others as students need to explain how they know.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten meet expectations that materials use accurate mathematical terminology. In the Instructional Resources Grade K, there are vocabulary cards for each chapter.

At the beginning of each chapter, there are vocabulary cards in the student materials that have the word on one side, and a model of the word on the other. In the teaching materials, there are instructions for use. For example, on page 2, the materials state, “Offer envelopes or small bags for students to store their vocabulary cards. Students can reference these cards as needed throughout the chapter.” Also on this page, the materials provide an activity to do with the students, “Have the students repeat as you say and show a vocabulary word and model the action provided below. To demonstrate the count card, hold up one hand and act like you are counting on your fingers to five. The number card can be acted out by pointing to a sign in the room that has a number on it. Stomp or clap to act out the numbers 1 through 5. Use a closed hand for 0. For the five frame card, draw and then point to a five frame on the board. Have students get in line to act out the order card.”

The following are examples where the materials use precise vocabulary with the students:

Chapter 2, Lesson 4, Laurie’s Notes, Teaching Notes, “How do you know the groups are not equal?” This problem gives students an opportunity to use language and definitions accurately, but does not give students the opportunity to use mathematical symbols as students are not yet using symbols with the mathematics they are learning at this point in Kindergarten.

Chapter 2, the beginning of chapter materials state, “Students lay their vocabulary cards in front of them with the picture side facing up. Show students a vocabulary card, say the word, and describe the picture definition. Students find the corresponding card. Students tell their partners how they know the picture is a match to the vocabulary word.”

Chapter 3, Lesson 5, Attend to Precision, states, “Have students use precise language to explain how they count. Ask, ‘How can you find out whether there are eight objects in a group?’ ‘How can you use counters to help you count the objects?’”

Chapter 4, Lesson 1, Laurie’s Notes, Think and Grow, “How do you know the groups are equal?” Listen for an understanding that the quantities are the same.

Chapter 7, the beginning of chapter materials start with a “Vocabulary Review”, reviewing the words “parts, whole, and number bond”. Included is an activity for the new vocabulary words, “Say a vocabulary word and then pass the echo ball to a student. The student echoes, or repeats the word, and then passes the echo ball back to you. Students need to listen carefully to repeat the word correctly. Consider challenging the students by having them define the words after they echo them.”

Chapter 7, Lesson 9, Laurie’s Notes, Think and Grow, MP6 is identified and the materials state, “When students say ‘4 take away 4 is none,’ acknowledge their correct thinking and say, ‘The number for none is 0. So 4 take away 4 is 0.’”

Chapter 8, Lesson 3, Laurie’s Notes, Think and Grow, Attend to Precision, “Students may write 5 = 10 + 15. They did not pay attention to the symbols already written, or are confused about the equal sign and addition symbol. Ask the student(s) to explain what their addition sentence means.”

Chapter 9,“Vocabulary Review”. Students review the words “equal” and “greater than”. Then, “Have students lay out their vocabulary cards in front of them with the picture side facing up. Say the word on the vocabulary card, show the word, and describe the picture definition to students. Have students find the corresponding card. Have students take turns showing the card and telling a partner about the word and its picture definition.”

Chapter 9, end of chapter materials, has a game called “Number Boss”. MP6 is identified and the materials state, “As you played the game, how did you know if the numbers were equal or not equal? How did you know who had the greater number?”

Gateway Three

Usability

Not Rated

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.

N/A

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

N/A

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

N/A

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

N/A

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

N/A

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

N/A

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

N/A

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

N/A

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

N/A

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

N/A

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

Criterion 3m - 3q

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

N/A

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.

N/A

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

N/A

Indicator 3p

Materials offer ongoing formative and summative assessments:

N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.

N/A

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

N/A

Indicator 3q

Materials encourage students to monitor their own progress.

N/A

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

N/A

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.

N/A

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

N/A

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

N/A

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.

N/A

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.

N/A

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.

N/A

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

N/A

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

N/A

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

N/A

Indicator 3ac

Materials can be easily customized for individual learners.
i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

N/A

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

Indicator Specific item that reviewers look for in materials.

Criterion Combination of all of the individual indicators for a single focus area.

Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.

Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

Focus and Coherence

Rigor and Mathematical Practices

Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

K-8 Math

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.